A sample of size n = 26 is used to perform a significance test for H0 : µ = 0 ve

Question

A sample of size n = 26 is used to perform a significance test for H0 : µ = 0 versus Ha : µ ? 0. The test statistic is t = 3.38.

Use 3 decimal places for t values and 2 decimal places for p-values.

A.What are the degrees of freedom for this statistic? Response:

B. Give the two critical values t* from the t table that bracket t = 3.38. What is the lower limit for 3.38 in the t table ? Response:

C.What is the upper limit for 3.38 in the t table ? Response:

D. What are the right-tail probabilities p for these two limits? What is the right-tail probability for the lower limit? Response:

E.What is the right-tail probability for the upper limit? Response:

F.Between what two values does the p-value of the test fall? What is the upper limit for the p-value of the test? Response:


G.What is the lower limit for the p-value of the test? Response:

H.For t = 3.38 and level of significance = 5%, what would your conclusion be? Reject H0 or Fail to reject H0


I. For t = 3.38 and level of significance = 1%, what would your conclusion be?
Reject H0 or Fail to reject H0

Explanation / Answer

A)
The degrees of freedom is, df=n-1
=26-1
df=25.

B)

The two critical values are given by,t*=±2.060.

The lower limit for the t-table is 3.078.

c)

The upper limit for the t-table is 3.45.

d)

The right tail probabilities are based on the level of signficance, we take i.e., 0.975 and 0.995.

and for the lower limit, the right-tail probability is P(t>3.078)=1-P(t<3.078)

=1-0.9975

=0.0025

e)

For the upper limit, the right-tail probability is P(t>3.45) =1-P(t<3.45)

=1-0.9995

=0.001.

f)

The p-value is between 2(0.0025) and 2(0.001)

=0.001<P-value<0.005.

The upper limit for the P-value of the test is 3.45.

g)

The lower limit for the P-value of the test is 3.078

h)

Since the P-value<=0.05. We reject Ho. The conclusion is is not zero.

i)

Since the P-value<=0.01. We reject Ho. The conclusion is is not zero.

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